Abstract
SummarySound design for experiments on soil is based on two fundamental principles: replication and randomization. Replication enables investigators to detect and measure contrasts between treatments against the backdrop of natural variation. Random allocation of experimental treatments to units enables effects to be estimated without bias and hypotheses to be tested. For inferential tests of effects to be valid an analysis of variance (anova) of the experimental data must match exactly the experimental design. Completely randomized designs are usually inefficient. Blocking will usually increase precision, and its role must be recognized as a unique entry in an anova table. Factorial designs enable questions on two or more factors and their interactions to be answered simultaneously, and split‐plot designs may enable investigators to combine factors that require disparate amounts of land for each treatment. Each such design has its unique correct anova; no other anova will do. One outcome of an anova is a test of significance. If it turns out to be positive then the investigator may examine the contrasts between treatments to discover which themselves are significant. Those contrasts should have been ones in which the investigator was interested at the outset and which the experiment was designed to test. Post‐hoc testing of all possible contrasts is deprecated as unsound, although the procedures may guide an investigator to further experimentation. Examples of the designs with simulated data and programs in GenStat and R for the analyses of variance are provided as File S1.Highlights Replication and randomization are essential for sound experimentation on variable soil. Analyses of variance of data from experiments must match the experimental designs. Experiments should be designed to answer preplanned questions and test hypotheses. Efficiency can be gained by blocking and factorial combinations of treatments.
Highlights
We describe in detail below the commonest and most straightforward designs, starting with the simplest, completely randomized schemes, introducing blocking, and progressing to factorial and split-plot designs
When assessing an experiment both the reviewers and, readers must be able to see that the experiment as described in the methods section accords with the anova reported in the results
Mean values for the sites sampled might be estimated precisely, but differences between practices or environments would not be. If the latter are not replicated, perhaps because replication was impossible, the investigator can say at the end only by how much the sites themselves differ from one another; any inference about the populations they represent cannot be based on the statistics
Summary
Sound design for experiments on soil is based on two fundamental principles: replication and randomization. Inference from the analysis of an experiment like that above is based on assumptions about the distribution of random quantities under the null hypothesis that are justified by that design, the way it was laid out in the field, glasshouse or laboratory and on the numbers of the degrees of freedom for the variance ratio. In this sense the analysis (and anova table) match the design. When assessing an experiment both the reviewers and, readers must be able to see that the experiment as described in the methods section accords with the anova reported in the results
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